The following figure-I .427 shows a block of mass m suspended from a fixed point by means ofa vertical spring. The block is oscillating simple harmonically and carries a charge q. There also exists a uniform electric field in the space. Consider four different cases. The electric field is zero, in case-I, `E= mg//q` downward in case-2, `E = mg// q` upward in case-3 and `E = 2mg//q` downward in case-4. The speed at mean position of block is same in all cases. Select which of the following statements is/ are correct :

Options

A. Time periods of oscillation are equal in case-1 and case-3
B. Amplitudes of displacement are same in case-2 and case-3
C. The maximum elongation (increment in length from natural length) is maximum in case-4.
D. Time periods of oscillation are equal in case-2 and case-4

Answer

A, B, C, D

Explanation

(A) Only equilibrium position changes. Time period remains same `T=2pi sqrt(m/k)`
(B) `1/2kx^(2)=1/2mv^(2)` :. V at mean position is same amplitude will be same.
(C) In case -4 Eaquilibrium position `x_(0)=(3mg)/k`